Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
Wayne HuFebruary 2006, NRAO, VA
(or why H0 is the Dark Energy)
Dark Energy in Light of the CMB
If its not dark, it doesn't matter!• Cosmic matter-energy budget:
Dark Energy
Dark Matter
Dark Baryons
Visible Matter
Dark Neutrinos
CMB Cornerstone• CMB temperature and polarization measures provide the high redshift cornerstone to cosmological inferences on the dark matter and dark energy
WMAP: Bennett et al (2003)
Multipole moment (l)
l(l+1
)Cl/2
π (µ
K2 )
Angular Scale
00
1000
2000
3000
4000
5000
6000
10
90 2 0.5 0.2
10040 400200 800 1400
� ModelWMAPCBIACBAR
TT Cross PowerSpectrum
Is H0 Interesting?• WMAP infers that in a flat Λ cosmology H0=72±5• Key project measures H0=72±8• Are local H0 measurements still interesting?
Is H0 Interesting?• WMAP infers that in a flat Λ cosmology H0=72±5• Key project measures H0=72±8• Are local H0 measurements still interesting?
• YES!!!
• CMB best measures only high-z quantites: distance to recombination energy densities and hence expansion rate at high z
Is H0 Interesting?• WMAP infers that in a flat Λ cosmology H0=72±5• Key project measures H0=72±8• Are local H0 measurements still interesting?
• YES!!!
• CMB best measures only high-z quantites: distance to recombination energy densities and hence expansion rate at high z
• CMB observables then predict H0 for a given hypothesis about the dark energy (e.g. flat Λ) • Consistency with measured value is strong evidence for dark energy and in the future can reveal properties such as its equation of state if H0 can be measured to percent precision
CMB Acoustic Oscillations
In the Beginning...
Hu & White (2004); artist:B. Christie/SciAm
Gravitational Ringing• Potential wells = inflationary seeds of structure
• Fluid falls into wells, pressure resists: acoustic oscillations
Seeing Sound• Oscillations frozen at recombination
• Compression=hot spots, Rarefaction=cold spots
Peaks in Angular Power• The Anisotropy Formation Process
Extrema=Peaks• First peak = mode that just compresses
• Second peak = mode that compresses then rarefies
Θ+Ψ
∆T/T
−|Ψ|/3 SecondPeak
Θ+Ψ
time time
∆T/T
−|Ψ|/3
Recombination RecombinationFirstPeak
k2=2k1k1=π/soundhorizon
• Third peak = mode that compresses then rarefies then compresses
Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scale by simple projection according to the angulardiameter distance DA
θA = λA/DA
`A = kADA
Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scale by simple projection according to the angulardiameter distance DA
θA = λA/DA
`A = kADA
• In a flat universe, the distance is simply DA= D ≡ η 0− η∗ ≈ η0, thehorizon distance, and kA = π/s∗ =
√3π/η∗ so
θA ≈η∗η0
Peak Location• Fundmental physical scale, the distance sound travels, becomes an
angular scale by simple projection according to the angulardiameter distance DA
θA = λA/DA
`A = kADA
• In a flat universe, the distance is simply DA= D ≡ η 0− η∗ ≈ η0, thehorizon distance, and kA = π/s∗ =
√3π/η∗ so
θA ≈η∗η0
• In a matter-dominated universe η ∝ a1/2 so θA ≈ 1/30 ≈ 2◦ or
`A ≈ 200
CMB & the Dark Energy• Universe is neither fully matter dominated at recombination nor at
the present due to radiation and dark energy
• Given a recombination epoch a∗ (depends mainly on temperatureand atomic physics) calculate the sound horizon
s∗ ≡∫
csdη =
∫ a∗0
dacs
a2H
note that this depends mainly on the expansion rate H at a∗, i.e.the matter-radiation ratio and secondarily on the baryon-photon ratio.
• Given a dark energy model, calculate the comoving distance to a∗
D =
∫ 1a∗
da1
a2H
• Given a curvature calculate the angular diameter distanceDA = R sin(D/R)
Dark Energy in the Power Spectrum• Features scale with angular diameter distance
• Small shift but angle already measured to
Calibrating Standard Ruler
Baryon & Inertia• Baryons add inertia to the fluid
• Equivalent to adding mass on a spring
• Same initial conditions
• Same null in fluctuations
• Unequal amplitudes of extrema
time ∆
T
Low Baryons
–
A Baryon-meter• Low baryons: symmetric compressions and rarefactions
time ∆
T
Baryon Loading
–
A Baryon-meter• Load the fluid adding to gravitational force
• Enhance compressional peaks (odd) over rarefaction peaks (even)
time|
| ∆
T
A Baryon-meter
• Enhance compressional peaks (odd) over rarefaction peaks (even)
e.g. relative suppression of second peak
Baryons in the Power Spectrum
Radiation and Dark Matter• Radiation domination: potential wells created by CMB itself
• Pressure support ⇒ potential decay ⇒ driving
• Heights measures when dark matter dominates
Driving Effects and Matter/Radiation
• Potential perturbation: k2Ψ = –4πGa2δρ generated by radiation• Radiation → Potential: inside sound horizon δρ/ρ pressure supported
δρ hence Ψ decays with expansion
Θ+Ψ
−Ψ
η∆T
/T
Hu & Sugiyama (1995)
Driving Effects and Matter/Radiation
• Potential perturbation: k2Ψ = –4πGa2δρ generated by radiation• Radiation → Potential: inside sound horizon δρ/ρ pressure supported
δρ hence Ψ decays with expansion• Potential → Radiation: Ψ–decay timed to drive oscillation
–2Ψ + (1/3)Ψ = –(5/3)Ψ → 5x boost• Feedback stops at matter domination
Θ+Ψ
−Ψ
η∆T
/T
Hu & Sugiyama (1995)
Driving Effects and Matter/Radiation
• Potential perturbation: k2Ψ = –4πGa2δρ generated by radiation• Radiation → Potential: inside sound horizon δρ/ρ pressure supported
δρ hence Ψ decays with expansion• Potential → Radiation: Ψ–decay timed to drive oscillation
–2Ψ + (1/3)Ψ = –(5/3)Ψ → 5x boost• Feedback stops at matter domination
Θ+Ψ
−Ψ
η∆T
/T
Hu & Sugiyama (1995)
Dark Matter in the Power Spectrum
Fixing the Past; Changing the Future
Fixed Deceleration Epoch• CMB determination ofmatter densitycontrols all determinations
in thedeceleration(matter dominated) epoch
• Current status:Ωmh2 = 0.14± 0.01 → 7%
• Distanceto recombinationD∗ determined to147% ≈ 2%
• Expansion rateduring any redshift in the deceleration epochdetermined to 7%
• Distanceto any redshiftin the deceleration epoch determined as
D(z) = D∗ −∫ z∗
z
dz
H(z)
• Volumesdetermined by a combinationdV = D2AdΩdz/H(z)
• Structurealso determined by growth of fluctuations fromz∗• Ωmh2 can be determined to∼ 1% in the future.
Value of Local Measurements• With high redshifts fixed, the largest deviations from the dark
energy appear at low redshift z ∼ 0• By the Friedman equation H2 ∝ ρ and difference between H(z)
extrapolated from the CMB H0 = 37 and 72 is entirely due to thedark energy in a flat universe
• With the dark energy density fixed by H0, the deviation from theCMB observed D∗ from the ΛCDM prediction measures theequation of state (or evolution of the dark energy density)
pDE = wρDE
• Intermediate redshift dark energy probes can then test flatnessassumption and the evolution of the equation of state: e.g.
w(a) = w0 + (1− a)wa
H0 = Dark Energy• Flat constant w dark energy model• Determination of Hubble constant gives w to comparable precision
• For evolving w, equal precision on average or pivot w, equally useful for testing a cosmological constant
-1
0.7
0.6
0.5
-0.8 -0.6 -0.4wDE
ΩDEh
Forecasts for CMB+H0• To complement CMB observations with Ωmh2 to 1%, an H0 of ~1% enables constant w measurement to ~2% in a flat universe
σ(lnH0) prior
σ(w
)
Planck: σ(lnΩmh2)=0.009
0.010.01
0.1
0.1
Sensitivity in Redshift• Fixed distance to recombination DA(z~1100) • Fixed initial fluctuation G(z~1100)• Constant w=wDE; (ΩDE adjusted - one parameter family of curves)
∆DA/DA
∆G/G
∆H-1/H-1
∆wDE=1/30.1
0
0.1
0.2
-0.2
-0.1
1z
Sensitivity in Redshift• SNIa high-z distance useful because it fixes the Hubble constant!
decelerationepoch measuresHubble constant
∆DA/DA
∆(H0DA)/H0DA
∆H0/H0∆G/G
∆H-1/H-1
∆wDE=1/30.1
0
0.1
0.2
-0.2
-0.1
1z
Evolution of the Dark Energy
Beyond Testing Λ• In the context of testing a cosmological constant, constraining a
constant w in a flat universe is the most important first test.
• CMB measurements are best complemented by H0.
• A deviation between the CMB predicted H0 and its measuredvalue in the form of a constant w 6= 1 is evidence against a flatΛCDM model.
• However it does not necessarily indicate a constant w 6= 1 flatmodel is correct! w is measured as its average or pivot value, asmall spatial curvature can change the expansion rate.
• A positive detection of deviations from ΛCDM will require morethan H0 to determine its physical origin.
• Investigate the role of H0 planning for success...
Sensitivity in Redshift• Three parameter dark energy model: w(z=0)=w0; wa=-dw/da; ΩDE • wa sensitivity; (fixed w0 = -1; ΩDE adjusted)
decelerationepoch measuresHubble constant
∆DA/DA
∆(H0DA)/H0DA
∆H0/H0∆G/G
∆H-1/H-1
∆wa=1/2; ∆w0=00.1
0
0.1
0.2
-0.2
-0.1
1z
Dark Energy Sensitivity• Three parameter dark energy model: w(z=0)=w0; wa=-dw/da; ΩDE • H0 fixed (or ΩDE); remaining w0-wa degeneracy• Note: degeneracy does not preclude ruling out Λ (w(z)≠-1 at some z)
decelerationepoch measuresHubble constant
∆DA/DA
∆(H0DA)/H0DA
∆G/G
∆H-1/H-1
∆wa=1/2; ∆w0=-0.150.1
0
0.01
0.02
-0.02
-0.01
1z
Dark Energy Sensitivity• H0 fixed (or ΩDE); remaining wDE-ΩT spatial curvature degeneracy• Growth rate breaks the degeneracy anywhere in the acceleration regime including local measurements!
decelerationepoch measuresHubble constant
∆DA/DA∆(H0DA)/H0DA
∆G/G
∆H-1/H-1
0.1
0
0.01
0.02
-0.02
-0.01
1z
∆wDE=0.05; ∆ΩT=-0.0033
Supernovae
Discovery of Acceleration• Distance-redshift to supernovae Ia indicates cosmological dimming (acceleration)
compilation from High-z team
Supernova Cosmology Project
34
36
38
40
42
44
Ωm=0.3, ΩΛ=0.7
Ωm=0.3, ΩΛ=0.0
Ωm=1.0, ΩΛ=0.0
m-M
(m
ag)
High-Z SN Search Team
0.01 0.10 1.00z
-1.0
-0.5
0.0
0.5
1.0
∆(m
-M)
(mag
)
Forecasts for CMB+H0+SNIa• Supernova Ia (2000 out to z=1) with curvature marginalized statistical errors only
w0
wa
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%3%1%
H0
Baryon Acoustic Oscillations
Cosmological Distances• Modes perpendicular to line of sight measure angular diameter distance
Local: Eisenstein, Hu, Tegmark (1998) Cosmological: Cooray, Hu, Huterer, Joffre (2001)
k (Mpc–1)0.05
2
4
6
8
0.1
Pow
er
Observedl DA-1
CMB provided
DA
Cosmological Distances• Modes parallel to line of sight measure the Hubble parameter
Eisenstein (2003); Blake & Glazebrook (2003); Hu & Haiman (2003); Seo & Eisenstein (2003)k (Mpc–1)
0.05
2
4
6
8
0.1
Pow
er
ObservedH/∆z
CMB provided
H
BAO Detection in SDSS• Baryon oscillations detected in 2-pt correlation function
Eisenstein et al (2005)
Forecasts for CMB+H0+BAO• Baryon oscillations (2000deg2 out to z=1.3 with spectroscopy) with curvature marginalized statistical errors only
w0
wa
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
Cluster Abundance
Cluster Abundance• Abundance of rare massive dark matter halos exponentially sensitive to the growth of structure
• Dark energy constraints if clusters can be mapped onto halos
0.001
0.01
0.1
1
10
1011 1012 1013 1014 1015
Mh (h-1M )
M*
ρ0
dnhd ln Mh N(Mh)
msAs
Mth
σlnM
z=0
Forecasts for CMB+H0+Clusters• Galaxy clusters (4000deg2 out to z=2 with photometric redshifts) with curvature marginalized statistical errors only
w0
wa
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
Weak Gravitational Lensing
Lensing Observables• Correlation of shear distortion of background images: cosmic shear• Cross correlation between foreground lens tracers and shear: galaxy-galaxy lensing
cosmicshear
galaxy-galaxy lensing
Halos and Shear
Forecasts for CMB+H0+Lensing• Weak lensing (4000deg2 out to zmed=1 with photometric redshifts) with curvature marginalized
w0
wa
-1.2
-0.4
-0.2
0
0.2
0.4
-1.0 -0.8
11%
3%
1%
H0
1500 13001400
1
2
3
4
0
Flux
Den
sity
(Jy)
550 450 -350 -450
0.1 pc
2.9 mas
10 5 0 -5 -10Impact Parameter (mas)
-1000
0
1000
2000
LOS
Vel
ocity
(km
/s)
Herrnstein et al (1999)NGC4258
Prospects for Percent H0• Improving the distance ladder with SNIa (~3%, Riess 2005) • Water maser proper motion, acceleration (~3%, VLBA Condon & Lo 2005; ~1% SKA, Greenhill 2004)
• Gravity wave sirens (~2% - 3x Adv. LIGO + GRB sat, Dalal et al 2006)• Combination of dark energy tests: e.g. SNIa relative distances: H0D(z) and baryon acoustic oscillations D(z)
Summary• CMB fixes energy densities, expansion rate and distances in the deceleration epoch • Strongest deviations due to the dark energy appear locally at z=0
• The single best complement to the CMB observables is H0 for a flat cosmology in determining deviations in the equation of state from a cosmological constant• Precision in H0 equal to CMB Ωmh2 optimal: 1% (masers, gw,..?)
• H0 also improves the ability of any single intermediate redshift dark energy probe (SNIa, BAO, Clusters, WL) to measure the evolution in the equation of state even in the SNAP/LST era• Combinations of dark energy probes can themselves indirectly determine H0
gotoend: List Box4: []